Re: [Fis] Group Theory, Quantum Mechanics, and Music

Dear Jerry and colleagues,

Some of the questions raised in your posting are really poignant.

>I am unaware of any specific process or logic that starts from mechanical
>principles and generates chemical structures. Quantum mechanics is based
>on the notion that if one starts from a chemical structure, one can, in
>some cases, generate a mechanical view of the molecule.

At the elementary level at which I can argue, 'physical chemistry' is the
theoretical field --mostly developed by Linus Pauling-- that forged the
link between quantum mechanics and theoretical chemistry. The central
conceptualizations of that field revolve around symmetry and symm-breaking
and are handled by means of group theory. A good summary on the successive
abstractions which are necessary to get the molecular viewpoint from the
principles of quantum mechanics can be found in Klaus Mainzer "Concepts of
Symmetry and the Unity of Science" (Walter de Gruyer, 1991), starting from
the Lorentz-invariant QM and the Galilei-invariant QM, following the
Born-Openheimer procedure to achieve 'atoms', and the Hartree-Fock
approximation to shared electron orbitals. The author discusses the whole
series of theoretical steps (badly summarized here) as one of the greatest
historical successes in theoretical reduction... And I think he is
partially right! Looking for the blind spots of mechanical thinking --as I
agree we should do, and I share some of your further points-- does not mean
that we should look aside of their monumental achievements.

>If the concept of music is the same as the concept of a group, what is the
>generative role of an individual's CNS in creating the emotional response
>to a particular song / piece / performance? Or, what distinguishes two
>individual's response to the same music?

I propose that we strongly distinguish between musical creation (in a
written form) and specialized performance on the one side, versus the
sensation and 'feeling' of music on the other. There is a very big
asymmetry in between both aspects of the musical phenomenon: action /
sensation. Deep formal training and a lot of practice are needed to achieve
well-wrought structures in the former, while most of the sensation/feeling
goes for 'free'. Clearly, numerous instances of the former may be properly
represented by the group theory tools (some of the very groups above) and
apart from Michael there is a number of musicological sudies about that
--see for instance the ISIS journal Symmetry, 1999, Vol 9, 1-2 (Arthur
Loeb, Dalia Cohen, Irina Guletsky, etc. For those interested in the
biological origins of music, there is also theor. group studies on bird and
whales songs. (eg, Dalia Cohen herself on birds).

The sentience of music follows another path, apparently quite distant. As I
have mentioned several times, the "essentic forms" of Manfred Clynes are
one of the few extended hypothesis. It has defects, and an ugly commercial
orientation (spurious I think) towards biomusical healing; but
unfortunately I am ignorant about other interesting approaches. Besides, in
my studies on laughter, in collaboration with Adrian Benitez from Mexico
who is visiting here (and also JA Bea, both in this list), we are finding
strong hints about the meaningfulness of these sentic forms in the
different 'musical forms' of laughter. Interested parties may have a glance
at a website that explores quite many (disconnected!) artistic aspects
related to sentic forms: http://www.wavecrest.org.uk/wavecrest/Sentic%201a2.htm
Sentic forms are some sort of elementary curves, with a resemblance to
natural landscapes of peaks and valleys (say, virtual landscapes putting
together coupled distributions of neural excitation/inhibition). One of the
possibilities we consider is the study of some of the sentic forms
underlying laughter by means of Michael's 'process grammar' (could then the
circle be closed, and light be thrown onto the primary steps of musical
sensory processing by 'groups' somehow mirroring the motor ones???) Pure
speculation, I admit.

>It goes without saying that mechanical thinking is extraordinarily useful
>for solving mechanical problems. Our challenge, it seems to me, is
>distinguishing mechanical from non mechanical problems. In earlier posts
>I referred to this distinction as the difference between Shannon
>information and human communication. Speciation of relations?

The reflection is very much in common. But I think that at the time being
we cannot unwound or untie the Gordian knot at the thick place you suggest.
We should attempt cutting it at a thinner place: the living cell. My
opinion is that our common task of advancing a new "informational
explanatory framework", beyond the limitations of the mechanical, is a very
complex, generational challenge. Actually it involves upturning and
repositioning quite many conceptual stepping-stones, and not just targeting
a new formalism (be it group theory, partitions, category theory, Boolean
nets, non-euclidean counting, deterministic chaos, power laws, etc., all of
them may be relevant to the info explanat. framework!). So the long-term
importance of attracting interdisciplinary people to the list, and keeping
patiently mixing our speculative ideas in very different fields...

best wishes

Pedro

PS. Recent movements in the list: Inputs of SCOTT (through John Collier)
and ADRIAN (through myself). Unfortunately EDWINA left several weeks ago
(she made no comments). We are around 90 people now.
   

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Received on Fri Jun 13 13:36:35 2003